I find Hal Abelson's book Turtle Geometry [1] fascinating. It describes a dialect of Logo (the graphical routines could probably be implemented relatively easily in Python/Tkinter or Tcl/Tk or something like Processing).
Once the basics are described, then it uses them to go on to explore things like non-euclidian geometry (and maybe topology?).
You might also want to check out http://GeoKone.NET, which is kinda similar, but not trying to imitate the original spirograph. But I hear many people have compared the two.
GeoKone is much more complex though and allows much more flexible geometry to be created.
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[ 4.0 ms ] story [ 60.9 ms ] threadanyone have a java applet that still runs? :o)
[edit: the source http://www.acooke.org/spiro.svg]
Once the basics are described, then it uses them to go on to explore things like non-euclidian geometry (and maybe topology?).
[1] http://www.amazon.com/Turtle-Geometry-Mathematics-Artificial...
If I had the time/inclination, a kickstarter based on the original toy that rendered on paper and screen might be an interesting plaything.
Another future angle could clearly involve 3d-printing of the disks.
Good stuff.
GeoKone is much more complex though and allows much more flexible geometry to be created.
http://alisey.deviantart.com/art/Orbits-316110768
http://explord.com/experiments/orbits/